{"as_of":"2026-08-20T13:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9c0a8b08069ca35c83170628975db01e4947f7ae13156cc4acee21012236deca","coverage":[{"denominator":22,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":22,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T12:28:07.708603Z","state":"measured"},{"denominator":22,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":22,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-20T06:33:59.587034+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/1908.07501/citation-record","integrity":"/paper/1908.07501/integrity","json":"/paper/1908.07501/citation-record.json","paper":"/paper/1908.07501"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.115167Z","title":"Ap´ ery,Irrationalit´ e deζ(2) et ζ(3), Ast´ erisque 61 (1979), 11–13","venue":null,"work_id":"2f58b402-27b4-4ac6-b0e0-a0b09c55dbab","year":1979},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.596944Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:fefc6bed487fbf75046a008108daaafdf9b3da4d4a009630e19c789025ebe9e3","observation_id":"54f71fb3-2280-4e4b-ad93-cea2b71c113f","resolution":{"observed_at":"2026-08-14T12:28:08.120029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.100334Z","title":"Beauville, Les familles stables de courbes elliptiques sur P1 admettant quatre ﬁbres singuli` eres , C","venue":null,"work_id":"b81d773e-411e-435b-8bf1-8dc6794bd4f9","year":1982},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.603328Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:c1a5e981f3c92506c9d93d2f7948d87fb06f5fc15a43f1914a287446137576bc","observation_id":"52128a35-a8cf-415a-a4a0-b68768eb4f0e","resolution":{"observed_at":"2026-08-14T12:28:08.105353Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.084628Z","title":"Bloch, H","venue":null,"work_id":"f2258376-2f12-4654-a5cf-a133053187ec","year":2004},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.607942Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:bd6c723022fc780b28a5cf0d992679b50222907f8decbc6278d82603ad030117","observation_id":"e59a2f25-4c90-4d48-bb38-a9fc097d55ff","resolution":{"observed_at":"2026-08-14T12:28:08.089468Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.069687Z","title":"Beukers, G","venue":null,"work_id":"f6629af6-f2bf-495e-a2a6-169cd6599de6","year":1989},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.612887Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:63f08c00405344e1f97cae9c27281070901fced8a3e96e8e66e85e8d91752f92","observation_id":"e1d81ce7-6772-456e-b47d-b7f593691083","resolution":{"observed_at":"2026-08-14T12:28:08.074210Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.055518Z","title":"Broadhurst, private communication","venue":null,"work_id":"f7ea86a4-4aa4-4357-a7bb-cd07599162cd","year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.618430Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:248a041707b88c7a1cb50b7ce19443680e2bcb110b2fe16d95d1cbfba9e54253","observation_id":"5864094c-3c5f-4b54-beff-71871bfeb2fb","resolution":{"observed_at":"2026-08-14T12:28:08.060885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.041794Z","title":"Fres´ an, P","venue":null,"work_id":"9d50760e-2c1d-49f6-a1dc-c7c74a4f581a","year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.624994Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:033f7ec8000deb7d212c0ecc5c7bc6bb47bbd9021b5060394411964182feec0a","observation_id":"f0f3dda0-5b3b-42f8-b600-34bfbb9f3bc1","resolution":{"observed_at":"2026-08-14T12:28:08.046274Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1404.7388","last_updated":"2014-04-29T15:01:03Z","snapshot_observed_at":"2026-08-14T23:35:53.434187Z","submitted_at":"2014-04-29T15:01:03Z","title":"The conifold point","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1404.7388","snapshot_observed_at":"2026-08-14T12:28:07.630136Z","title":"Galkin, The Conifold Point , ArXiv 1404.7388 Math.AG","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.630136Z"},"links":{"cited_paper":"/paper/1404.7388","citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:98f6ba2c0e4ab57111d4ed694af0b94b05b1c60a7d6c5bbc5bc454d0d7805776","observation_id":"0789a238-e0ef-4417-a3f0-8b08464f9b74","resolution":{"observed_at":"2026-08-14T12:28:07.630136Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.027951Z","title":"Golyshev, D","venue":null,"work_id":"644373cc-d2fc-4fe0-a3b2-f05c2d7b654b","year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.636167Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:2266a52e09ce1598a117ece98b9d1383d2231107b5464b3dc0bb0012f8d8f9f8","observation_id":"247f8857-72f0-4d59-b3b1-2452406537d0","resolution":{"observed_at":"2026-08-14T12:28:08.032436Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:08.012451Z","title":null,"venue":null,"work_id":"917dbd6c-49a6-4182-aeab-d640beff4081","year":1991},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.642123Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:31aa5cae5a261313f8db6cf44ef18af08de43444f03234ca136fd3dd4630a71a","observation_id":"21bfae49-f3cb-436c-8f2d-c89912cada45","resolution":{"observed_at":"2026-08-14T12:28:08.017414Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.985025Z","title":"Haeﬂiger, Local theory of meromorphic connections in dimension 1 (Fuchs theory), Chapter III in A","venue":null,"work_id":"8f7c97b2-0deb-4db1-a783-890a376316bd","year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.647583Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:57b3f4e99f1fa7f29e2630f2498ccef087b927b1d4039984eca61a29e972c738","observation_id":"0a3e9555-2c13-4f5b-814c-4a8061ba9ed5","resolution":{"observed_at":"2026-08-14T12:28:07.992221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.969557Z","title":"Illusie, Autour du th´ eor` eme de monodromie locale, Expos´ e I, P´ eriodesp-adiques - S´ eminaire de Bures, 1988","venue":null,"work_id":"d2f00350-89af-42ad-8976-4eb9e1cb02c0","year":1988},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.652609Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:577bedde3ecc2483679424f391adb7a2ee0e378bc62c38a50d688d9a26ae2fe3","observation_id":"6b8ba41c-9b17-4abc-ade7-88b880c77ee7","resolution":{"observed_at":"2026-08-14T12:28:07.974239Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.955496Z","title":"Katz, Nilpotent connections and the monodromy theorem : applicat ions of a result of Turrittin , Publications math´ ematiques de lI.H.´E.S","venue":null,"work_id":"ebcc1807-f31a-43b2-bb2a-68dc17d69009","year":1970},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.657728Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:2811e012e35bdae8f4b238de087242efa72494adcaea4b0a9ec033ffb2c40766","observation_id":"c98dbdd8-9446-4c58-a41b-3d38b5e0fe9c","resolution":{"observed_at":"2026-08-14T12:28:07.959868Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.938959Z","title":"Katz, On the calculation of some diﬀerential Galois groups , Invent","venue":null,"work_id":"ccdb823b-1115-44da-8120-d101f6e90727","year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.662221Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:460d4244a562b15381d5b4cc80eae07dbeb8d637b148ce486fd5863bdc8660b5","observation_id":"e7caa0e8-f56e-45cd-b23b-958c3b6ebff3","resolution":{"observed_at":"2026-08-14T12:28:07.943714Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1708.03836","last_updated":"2020-06-12T23:13:03Z","snapshot_observed_at":"2026-08-15T01:37:14.758273Z","submitted_at":"2017-08-13T01:51:29Z","title":"Motivic irrationality proofs","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1708.03836","snapshot_observed_at":"2026-08-14T12:28:07.666937Z","title":"Kerr, Motivic Irrationality Proofs , arXiv:1708.03836","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.666937Z"},"links":{"cited_paper":"/paper/1708.03836","citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:7c711992bf5a9a9fb9cfe46e5f2f30ae9f5527884396e31e7303ff6e9cb2d320","observation_id":"0eef0548-f3d0-4ea7-9101-ac54a7893389","resolution":{"observed_at":"2026-08-14T12:28:07.666937Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.923030Z","title":"Kerr, Unipotent extensions and diﬀerential equations (after Blo ch-Vlasenko), to appear","venue":null,"work_id":"54b8ab3d-7ce9-4f99-aa25-2f2096a0deff","year":null},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.671335Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:b31122d2dcf7414be338e0340d12e8ee52c05cfce5621c907ef2ed58762649ec","observation_id":"7d34ac78-9a31-4f8d-9947-207935993ba4","resolution":{"observed_at":"2026-08-14T12:28:07.928185Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.906648Z","title":"Kontsevich, D","venue":null,"work_id":"3f4a899f-71a6-4945-9e31-2272a41b964e","year":2001},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.676031Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:0786a1979673117ad6124cc18c115b49aa56e1f1c68771135684f3f7c51bdad2","observation_id":"5bfa8fb1-cd9a-454b-bb8d-031a2eb43a31","resolution":{"observed_at":"2026-08-14T12:28:07.912076Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.886066Z","title":"Loeser, C","venue":null,"work_id":"bbafe00c-032c-4f45-b62b-8376d2d4ca67","year":1991},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.681281Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:6377b4085f9c8af38249ed86a5e520088c8871c1176cdd8f292c13038aace28f","observation_id":"927924af-9f41-4be2-a239-fe5ee1928585","resolution":{"observed_at":"2026-08-14T12:28:07.892182Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.868992Z","title":"Malgrange, ´Equations Diﬀ´ erentielles ` a Coeﬃcients Polynomiaux, Birkh¨ auser, Progress in Math, vol","venue":null,"work_id":"45612398-a69a-4abc-9c47-f0b60660f28f","year":1991},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.686300Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:2e186f67899ba032f8753a3dd419b5bce9c61a18a3b5c56bdb492ec845b88855","observation_id":"f41f448d-8524-41dd-b7b5-32a0dba38bf9","resolution":{"observed_at":"2026-08-14T12:28:07.874137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.848428Z","title":"Peters, J","venue":null,"work_id":"3cabe963-8050-4820-9720-e700ad4d7c59","year":2007},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.691838Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:9eaaa00ed0beb9218cbbbc25440a24e6f53607eaed8d1031a6d45f6c0f10a206","observation_id":"eea26584-efa2-4092-b502-b3376949e779","resolution":{"observed_at":"2026-08-14T12:28:07.855647Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.829480Z","title":"Schmid, Variation of Hodge Structure: the Singularities of the Peri od Mapping , Inventiones Math","venue":null,"work_id":"45394bf0-6e9e-47d3-8592-0b55bd50dd67","year":1973},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.697152Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:6d777fffaad1d047cf0037e4ac6eae825e28224f621b76d6070eaff8c06e1147","observation_id":"0ef36fbf-c0c4-49fb-9036-f36b4fc52103","resolution":{"observed_at":"2026-08-14T12:28:07.834303Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.809584Z","title":"Steenbrink, Limits of Hodge Structures , Inventiones Math","venue":null,"work_id":"e5515202-624c-4494-be6e-677c785c2a70","year":1976},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.703134Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:927fcbd949f0068707ff4a46670db0da0f7062340dc716926739000079a852a7","observation_id":"a1926562-7f71-4cb3-9956-86404a8b8701","resolution":{"observed_at":"2026-08-14T12:28:07.816933Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T12:28:07.780047Z","title":"Zagier, Integral solutions of Ap´ ery-like recurrence equations , in Groups and symmetries , vol- ume 47 of CRM Proc","venue":null,"work_id":"72dad3c1-995b-4527-a5b1-7e26445d8271","year":2009},"citing_paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T12:28:07.708603Z"},"links":{"citing_paper":"/paper/1908.07501"},"observation_digest":"sha256:81d986255a51021ed76d57c4427585411031f794e0078f1116709174e953e9e3","observation_id":"90498b5d-05e4-48d9-83e6-166a9595fd1f","resolution":{"observed_at":"2026-08-14T12:28:07.787293Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.07501","last_updated":"2020-06-23T07:19:12Z","latest_version":2,"primary_category":"math.NT","snapshot_observed_at":"2026-08-19T00:31:58.347114Z","submitted_at":"2019-08-20T17:26:29Z","title":"Gamma functions, monodromy and Frobenius constants"},"reference_resolution":{"displayed":22,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":3,"verified_exact":0,"verified_fuzzy":19},"total_outbound_references":22},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-20T06:33:59.587034+00:00","source":"crossref"},{"observed_at":"2026-08-20T06:33:54.927442+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:1908.07501."}